Question

lf the circles of same radius ${}^{\prime }{a}^{\prime }$ and centres at $(2,-3)$ , $(5,6)$ cut orthogonally then $a=$

• A. $4$
• B. $4\sqrt{2}$
• C. $3\sqrt{5}$
• D. $3$

Answer 1

The correct option is C $3\sqrt{5}$

If two circles are orthogonal to each other then,
$r{{}_1}^2+r{{}_2}^2=(c_1{c}_2{)}^2$
Given $r_1=r_2=r$ and $c_1=(2,-3),c_2=(5,6)$
So, $2r^2=(\sqrt{9+81}{)}^2$
$\Rightarrow r^2=45$
$\Rightarrow r=3\sqrt{5}$